Practice Test 5 - ACT Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. A student wants a single logarithm equivalent to $\ln(12)-\ln(3)$. Which expression is equivalent?
2. A quality check requires the error $x$ to be at least 3 units away from 2. Which values of $x$ satisfy $|x-2|\ge 3$? Give the solution set in interval notation.
3. Which of the following is the product $AB$ if $A = \begin{bmatrix} 2 & 3 \\ 1 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 4 \\ 0 & -1 \end{bmatrix}$?
4. In triangle JKL, angle J measures 90°, angle K measures 30°. What is the measure of angle L?
5. A savings account earns simple interest according to the equation $A = 1000 + 50t$, where $A$ is the amount in dollars and $t$ is the number of years. How much interest is earned after 5 years?
6. A triangle has side lengths $7$, $24$, and $25$. Which describes the triangle? (Choose from: right, isosceles, equilateral, scalene.)
7. If the ratio of cats to dogs in a shelter is 3:5 and there are 15 cats, how many dogs are there?
8. Which polynomial is equivalent to $x(x - 1) + 2(x + 1)$?
9. Sarah bought 3 notebooks at $2 each and 5 pens at $1.50 each. Which expression represents the total cost?
10. A force is represented by the vector $\mathbf{v}=\langle 7,\,-4\rangle$. What is $3\mathbf{v}$?
11. What is the magnitude of $\mathbf{b} = \langle 0, -13 \rangle$?
12. Lines $m$ and $n$ are parallel, and a transversal $t$ crosses them. The angle in the upper intersection that is above line $m$ and to the right of $t$ is $50^\circ$. The corresponding angle at the lower intersection (above line $n$ and to the right of $t$) is labeled $x$. m ⇒ ⇒ ⇒ / 50° / / n ⇒ ⇒ ⇒ / x If lines $m$ and $n$ are parallel, what is the measure of angle $x$?
13. A student must choose 2 electives from a list of 6 different electives. The order of the choices does not matter. How many different pairs of electives are possible?
14. A circle has a radius of 6 centimeters. What is the area, in square centimeters, of a sector of this circle that has a central angle of $\dfrac{2\pi}{3}$ radians?
15. A cone has diameter 8 units and height 6 units. What is the volume of the cone? (Use $\pi$ in your answer.)
16. Which equals $\tan(60^\circ)$?
17. A debate team consists of 8 students. The coach must select exactly 3 students to form a panel for an upcoming competition. How many different 3-student panels can be formed?
18. What is the value of $x$ in the proportion $\frac{3}{5}=\frac{x}{20}$? (Use cross-multiplication: if $\frac{a}{b}=\frac{c}{d}$, then $ad=bc$.)
19. In how many different ways can a committee of 4 be selected from a group of 7 people?
20. If $A = \begin{pmatrix} 0 & 2 \\ -3 & 1 \end{pmatrix}$, what is $2A$?

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